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random variables

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Published: 01 January 1997
Fig. 1 Interference plot for load and resistance random variables More
Image
Published: 01 January 1996
Fig. 4 Single-random-variable model of S - N variability More
Image
Published: 01 January 1996
Fig. 5 Two-random-variable model of S - N variability More
Image
Published: 01 January 2002
Fig. 13 Example: generating random variable values More
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006803
EISBN: 978-1-62708-329-4
... Abstract This article provides an outline of the issues to consider in performing a probabilistic life assessment. It begins with an historical background and introduces the most common methods. The article then describes those methods covering subjects such as the required random variable...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003514
EISBN: 978-1-62708-180-1
... Abstract This article describes the historical background, uncertainties in structural parameters, classifications, and application areas of probabilistic analysis. It provides a discussion on the basic definition of random variables, some common distribution functions used in engineering...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0009212
EISBN: 978-1-62708-176-4
... probability, random variables, degrees of freedom, confidence limits and intervals, and reliability. Descriptive statistics, measures of central tendency, confidence limits and intervals, and degrees of freedom are also discussed. degrees of freedom hypothesis testing probability random variables...
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002369
EISBN: 978-1-62708-193-1
... “Fundamentals of Modern Fatigue Analysis for Design” and “Estimating Fatigue Life” in this Volume. In general, uncertainty can be divided into random (or aleatory) and statistical (or epistemic) types. Quantities whose uncertainties are random have values that are inherently variable and can be described...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002431
EISBN: 978-1-62708-194-8
... be buckling, permanent deformation, tensile failure, fatigue cracking, loss of cross section due to wear, corrosion, or erosion, or fracture due to unstable crack growth. In any of these cases, the failure resistance of a large number of components of a particular design is a random variable, and the nature...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002476
EISBN: 978-1-62708-194-8
... and L are random variables. Under this assumption P f is the product of two finite probabilities summed over all possible outcomes. Both probabilities are associated with an event and a random variable. The first event is defined by the random variable L taking on a value in the range: (Eq 3...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0009219
EISBN: 978-1-62708-176-4
... Abstract This article reviews the planning of fatigue experiments, including the structure of a test plan, randomization, and nuisance variables. The statistical characterization of the S/N (stress/life) or e/N (strain/life) response of a single material tested under a single condition...
Book Chapter

Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003088
EISBN: 978-1-62708-199-3
... in one particular property, generally affects other properties simultaneously. Similar interrelations that are more difficult to characterize exist among the various mechanical and physical properties and variables associated with manufacturing processes. For example, cold drawing a wire to increase its...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005505
EISBN: 978-1-62708-197-9
... ] Calculation of the statistics and probabilities necessary to implement a stochastic optimization strategy requires the identification and characterization of random variables and the incorporation of a sampling strategy within the stochastic optimization search. Random variables are inputs to a simulation...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0009214
EISBN: 978-1-62708-176-4
... variables and simplifies the analysis of the results 3. As far as possible, the experiment should be free from bias (conscious or unconscious) Some variables may be taken into account by planned grouping; for other variables, use randomization; the use of replication aids randomization to do a better...
Image
Published: 01 January 1996
Fig. 12 Examples of more complex variable-amplitude load histories for fatigue tests. (a) Program loading with Lo-Hi-Lo sequence of S a′ (b) Randomized block loading. (c) Narrow-band random loading. (d) Broad-band random loading. (e) Simple flight simulation loading. All flights are equal More
Series: ASM Handbook
Volume: 17
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.hb.v17.a0006463
EISBN: 978-1-62708-190-0
... the average are represented by the random variable, ε: (Eq 3) g ( S ) = f ( a ) + ε A detection of the defect occurs if the signal exceeds a threshold, T . Assuming that the function g ( S ) is monotonically increasing, then S ≥ T if and only if g ( S ) ≥ g ( T ). Therefore...
Image
Published: 01 January 1989
Fig. 13 Surface characteristics of cast Inconel 718 (aged, 40 HRC) produced by EDM. (a) Finishing conditions produced a variable recast layer 0.005 mm (0.0002 in.) thick. 860×. (b) Roughing conditions produced an extensively cracked variable recast layer up to 0.05 mm (0.002 in.). The random More
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005512
EISBN: 978-1-62708-197-9
... a promising approach for a probabilistic model for the prediction of diffusion bonding time, based on the identification and characterization of deterministic variables and random variables. The probabilistic distribution of surface roughness is introduced into a deterministic model of diffusion bonding...
Series: ASM Handbook
Volume: 7
Publisher: ASM International
Published: 30 September 2015
DOI: 10.31399/asm.hb.v07.a0006088
EISBN: 978-1-62708-175-7
... gradients created by mixing, handling, transporting, or movement of materials. Segregation mechanisms that interfere with random motion of particles operate in combination, and reduction of industrial problems depends on minimizing the more severe ones ( Ref 1 ). Some of the variables affecting flow...
Series: ASM Handbook
Volume: 13A
Publisher: ASM International
Published: 01 January 2003
DOI: 10.31399/asm.hb.v13a.a0003641
EISBN: 978-1-62708-182-5
...) F ( x ) = ∫ f ( x ) d x = 1 − exp ( − λ x ) where λ is the constant hazard rate, and x is the measured variable. Poisson Distribution Typically, a Poisson random variable is a count of the number of events that occur in a certain time interval or spatial...